On the spectrum of A(Ω) and $H^∞(Ω)$

• Autorzy: Urban Cegrell
• Języki publikacji: EN

Abstrakty

EN

We study some properties of the maximal ideal space of the bounded holomorphic functions in several variables. Two examples of bounded balanced domains are introduced, both having non-trivial maximal ideals.

Słowa kluczowe

EN

bounded analytic function; spectrum; Gleason problem; balanced domain

Kategorie tematyczne

• 32A07: Special domains (Reinhardt, Hartogs, circular, tube)
• 32D10: Envelopes of holomorphy

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1993
• Tom: 58
• Numer: 2
• Strony: 193-199

Daty

wydano

1993

otrzymano

1992-11-05

Twórcy

autor

Urban Cegrell

• Department of Mathematics, Umeå University, S-901 87 Umeå, Sweden

Bibliografia

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• [2] J. E. Fornæss and N. Øvrelid, Finitely generated ideals in A(Ω), Ann. Inst. Fourier (Grenoble) 33 (2) (1983), 77-85.
• [3] T. W. Gamelin, Uniform Algebras, Prentice-Hall, Englewood Cliffs, N.J., 1969.
• [4] T. W. Gamelin, Uniform Algebras and Jensen Measures, Cambridge Univ. Press, 1978.
• [5] M. Hakim et N. Sibony, Spectre de A(Ω̅ ) pour les domaines bornés faiblement pseudoconvexes réguliers, J. Funct. Anal. 37 (1980), 127-135.
• [6] J. J. Kohn, Global regularity for ∂̅ on weakly pseudo-convex manifolds, Trans. Amer. Math. Soc. 181 (1973), 273-292.
• [7] A. Noell, The Gleason problem for domains of finite type, Complex Variables 4 (1985), 233-241.
• [8] M. Range, Holomorphic Functions and Integral Representations in Several Complex Variables, Springer, 1986.
• [9] N. Sibony, Prolongement analytique des fonctions holomorphes bornées, in: Sém. Pierre Lelong 1972-73, Lecture Notes in Math. 410, Springer, 1974, 44-66.
• [10] J. Siciak, Balanced domains of holomorphy of type $H^∞$, Mat. Vesnik 37 (1985), 134-144.
• [11] N. Øvrelid, Generators of the maximal ideals of A(D̅), Pacific J. Math. 39 (1971), 219-223.